Geodesic
Evaluations of Some Determinants of Matrices Related to the Pascal Triangle
Séminaire lotharingien de combinatoire, Tome 47 (2001-2002)

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We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence ai,j=ai-1,j+ai,j-1, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland Bacher [J. Théorie Nombres Bordeaux 14 (2002), 19-41].

Comment by the author: It is much easier to prove Theorem 4 by appealing to (the more general) Proposition 1 in the author's paper "Advanced Determinant Calculus," Séminaire Lotharingien Combin. 42 ("The Andrews Festschrift") (1999), Article B42q, 67 pp. 
@article{SLC_2001-2002_47_a6,
     author = {Christian Krattenthaler},
     title = {Evaluations of {Some} {Determinants} of {Matrices} {Related} to the {Pascal} {Triangle}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {47},
     year = {2001-2002},
     url = {http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a6/}
}
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Christian Krattenthaler. Evaluations of Some Determinants of Matrices Related to the Pascal Triangle. Séminaire lotharingien de combinatoire, Tome 47 (2001-2002). http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a6/